Because of the unique protocols of the measuring process used in each
technology, the precise steps to calculating flux must consider the specific
measuring system used.

We describe here the approach we use with the direct coupled amplifier
system produced by Applicable Electronics and with measurements taken with
either the 3DVIS software written by JG Kunkel or the ASET software from
SCIENCEWARES.

We provide a downloadable zipped MsExcel spreadsheet
which will aid in this process.
We also provide a downloadable zipped MathCAD worksheet
which will perform the same process.
Each measurement of flux at a point in space requires two measurements made
at that point in space (local probe voltage in mV and µV difference in the
direction of the flux) plus a set of constants that are a function of the
ion being measured, the LIX being used, the sampling protocol used by
the software and the measured efficiency of that particular protocol and
probe combination. We will detail how these numbers are measured and
how they are used to calculate flux.

The diffusion coefficient is tabulated for each ion but one must be
conscious of the fact that ions travel in pairs and the diffusion coefficient
in reality varies with concentration of the ion as well as the type and
concentrations of counter-ions [Diffusion coefficients in aqueous solutions
at 25°. Handbook of Chemistry and Physics, Chemical Rubber Co.].
This means that all flux measurements must be accepted with
reservations.

The spatial differential, dr, is represented in the calculation by the distance
between the points of the two discrete
concentration measurements and may consist of a single distance if a single
dimension of flux is being measured, or it may be made up of independent
axes (X, Y and/or Z) if vectors of flux in space are being calculated.
In general practice, individual axes of flux are calculated and then a resultant
flux is calculated using the hypotenuse square rule. This is
practical in all situations where the sources of ions are large and the
individual spatial differentials are small compared to the dimensions of the
source/sink being examined.

The concentration differential, dC, is a value that varies during an experiment
and requires the most attention. Each point in space where one decides to measure
flux, can be redefined temporarily as an origin of measurement with {x,y,z} =
{0,0,0}. At that point one needs to determine the concentration of the ion
of interest by using the mV potential measured at that point in combination
with the equation for concentration that has been previously determined for
that LIX and ion combination over a concentration span that spans the current
conditions:

C[0,0,0] = 10(mV[0,0,0] - A)/B
, where A,B = Nernst intercept, slope.&nbsp
Next the small measured differential voltage, µV, that results from moving
the probe in the chosen
direction (say dx of dx, dy, or dz) is measured by subtraction of the voltage
measured at {0,0,0} and {dx,0,0}. It is this voltage differential, measured over
a short time interval, that is subject to the efficiency correction that one has
established for this LIX, ion and sampling conditions. The desire to make
measurements in as short a time span as possible is in conflict with the time
constant of the LIX. The LIX has a irreducible time that it takes to reach
95% of its expected voltage in a particular ion concentration.
The Nernst callibration curve of mV vs ion concentration tells one the
expected mV for a particular ion concentration one can measure when the
probe is given abundant time to reach its theoretically correct voltage.
The efficiency callibration
tells one the percentage of the expected one can achieve during the dynamic
measuring process. In the enclosed
spreadsheet, knowing the efficiency corrected µV difference allows one
to calculate the concentration of the ion of interest at the small distance from
the origin {0,0,0}:

C[dx,0,0] =
10(mV[0,0,0]-µVdiff/1000*eff) - A)/B) ,

with A and B as above and eff = efficiency of measuring the
µV difference.&nbsp
Then dC can be calculated as:

dCx = C[dx,0,0] - C[0,0,0].

After the above calculations are performed on each of the dimensions involved,
one can proceed to finally calculate the flux:

Jx = D dCx/dr , and

perhaps plot Jx, Jy, and Jz as a vector in
space at the measurement point, or combine them according to the pythagorean
theorem into a joint/total flux: